State Characterization in Sampling Points and Representation of Velocity Fields by Nodal Values as a Basis for Discretization

Abstract

Continuum theory masks the fact that the concept of state pertains to a finite, be it very small neighbourhood of a material point. This neighbourhood is subjected to an average deformation, derived from the average motion of mass, that is described by the velocity field. In thermodynamic theory it is now generally realized that the stresses, dual to the local rates of deformation and that determine the rate of work of deformation, do not provide a sufficient description of the state of the material, in so far as this state is affected by deformation. Hidden, or internal state variables are needed in constitutive equations, that give a description of memory effects. It turns out that it is fruitful to enlarge the number of state variables without an increase of the number of independent kinematic variables. Apparently the description of the dissipative processes, responsible for the memory effects, tolerate a certain latitude in the description of the kinematics. In other words the effect of the thermodynamic processes in the different constituents overshadows the effect of disturbances of mechanical equilibrium among constituents, the number of equilibrium equations being equal to the number of kinematic variables.